7 6 entropy change in irreversible processes
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7.6 Entropy Change in Irreversible Processes

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7 6 entropy change in irreversible processes

7.6 Entropy Change in Irreversible Processes

  • It is not possible to calculate the entropy change ΔS = SB - SA for an irreversible process between A and B, by integrating dq / T, the ratio of the heat increment over the temperature, along the actual irreversible path A-B characterizing the process.

  • However, since the entropy is a state function, the entropy change ΔS does not depend on the path chosen.The calculation of an irreversible process can be carried out via transferring the process into many reversible ones:

  • Three examples will be discussed here: (1) heat exchange between two metal blocks with different temperatures; (2) Water cooling from 90 to a room temperature; (2) A falling object.


7 7 free expansion of an ideal gas

7.7 Free Expansion of an Ideal Gas


7 8 entropy change for a liquid or solid

7.8 Entropy Change for a Liquid or Solid


Thermodynamics potential

Thermodynamics Potential

Chapter 8


8 1 introduction

8.1 Introduction

  • Thermodynamic potentials: Helmholtz function F and the Gibbs function G.

  • The enthalpy, Helmholtz function and Gibbs functions are all related to the internal energy and can be derived with a procedure known as Legendre differential transformation.

  • The combined first and second laws read

    dU = Tds – PdV

    where T and S, and -P and V are said to be canonically conjugate pairs.

  • By assuming U = U(S,V), one has


8 2 the legendre transformation

8.2 The Legendre Transformation

  • Consider a function Z = Z(x, y), the differential equation is dZ = Xdx + Ydy

    where X and x, Y and y are by definition canonically conjugate pairs.

  • We wish to replace (x, y) by (X, Y) as independent variables. This can be achieved via transforming the function Z(x,y) into a function M(X,Y).

  • Assume M(X,Y) = Z(x,y) – xX – yY

    Then dM = dZ – Xdx – xdX –Ydy – ydY

    dM = -xdX - ydY


8 3 definition of the thermodynamic potentials

8.3 Definition of the Thermodynamic Potentials


8 4 the maxwell relations

8.4 The Maxwell Relations


8 5 the helmholtz function

8.5 The Helmholtz Function

  • The change in internal energy is the heat flow in an isochoric reversible process.

  • The change in enthalpy H is the heat flow in an isobaric reversible process.

  • The change in the Helmholtz function in an isothermal reversible process is the work done on or by the system.

  • The decrease in F equals the maximum energy that can be made available for work.


8 6 the gibbs function

8.6 The Gibbs Function

  • Based on the second law of thermodynamics

    dQ ≤ T∆S with dQ = ∆U + P ∆V

  • Combine the above expressions

    ∆U + P ∆V ≤ T∆S

    ∆U + P ∆V - T∆S ≤ 0

  • Since G = U + PV –TS

    (∆G)T,P≤ 0 at constant T and P

    or G f ≤ Gi

  • Gibbs function decreases in a process until a minimum is reach, i.e. equilibrium point.

  • Note that T and P need not to be constant throughout the process, they only need to have the same initial and final values.


8 7 application of the gibbs function to phase transitions

8.7 Application of the Gibbs Function to Phase Transitions


8 8 an application of the maxwell relations

8.8 An application of the Maxwell Relations


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